Factor by grouping.

12x^3-20x^2+3x-5

12x³ - 20x² + 3x - 5

4x² (3x) - 4x² (5) + 1 (3x) - 1 (5)

4x² (3x - 5) + 1 (3x - 5)

(4x² + 1) (3x - 5)

First, group them in 2's (2 numbers per group)

and see which ones have the factors of each other

you want to group 12x^3 with 3x because 3 is a factor of 12

then you want to group - 20x^2 and - 5 together becuase 5 is a factor of 20 so

(12x^3+3x) + (-20x^2-5)

undistribute

(3x) (4x^2+1) + (-5) (4x^2+1)

revese distribute (ab+ac=a (b+c))

(3x-5) (4x^2+1)